# continuous

## English

### Adjective

(

*-*)

Without break, cessation, or interruption; without intervening time.
*a ***continuous ** current of electricity

* **1847 **, , Ticknor and Fields (1854), page 90:
*he can hear its ***continuous ** murmur

Without intervening space; continued; protracted; extended.
*a ***continuous ** line of railroad

(botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
(analysis, of a function) Such that, for every *x'' in the domain, for each small open interval ''D'' about ''f''(''x''), there's an interval containing ''x'' whose image is in ''D *.
(mathematics, more generally, of a function) Such that each open set in the range has an open preimage.
*Each ***continuous ** function from the real line to the rationals is constant, since the rationals are totally disconnected.

(grammar) Expressing an ongoing action or state.
#### Usage notes

*
#### Synonyms

* (*without break, cessation, or interruption in time''): constant, continual (''but see usage notes above *), incessant, never-ending, ongoing, unbroken, unceasing, unending, uninterrupted
* (*without break, cessation, or interruption in space *): connected, unbroken
* See also
#### Antonyms

* (*without break, cessation, or interruption in time *): broken, discontinuous, discrete, intermittent, interrupted
* (*without break, cessation, or interruption in space *): broken, disconnected, disjoint, unbroken
* (*in mathematical analysis *): discontinuous, stepwise
#### Derived terms

* continuous brake
* continuous impost
* continuously
* continuousness
(*in mathematics*)
* continuous distribution
* continuous function
* continuous group
* continuous line illusion
* continuous map
* continuous mapping theorem
* continuous space
* continuous vector bundle
* continuously differentiable function
* uniformly continuous
#### Related terms

* continuity
* continued
* continuum
### See also

* constant
* contiguous
### References